Labeled binary planar trees and quasi-Lie algebras

Abstract

We study the natural map eta between a group of binary planar trees whose leaves are labeled by elements of a free abelian group H and a certain group D(H) derived from the free Lie algebra over H. Both of these groups arise in several different topological contexts. The map eta is known to be an isomorphism over Q, but not over Z. We determine its cokernel and attack the conjecture that it is injective.

This is the version published by Algebraic & Geometric Topology on 9 August 2006

References in corpus (4)

• Claspers and finite type invariants of links
• Homology cylinders: an enlargement of the mapping class group
• Calculus of clovers and finite type invariants of 3-manifolds
• Addendum and correction to: Homology cylinders: an enlargement of the mapping class group

Cited by in corpus (9)

• Higher Order Intersections in Low-Dimensional Topology
• Whitney tower concordance of classical links
• Tree homology and a conjecture of Levine
• Abelian quotients of the $Y$-filtration on the homology cylinders via the LMO functor
• Geometric Filtrations of Classical Link Concordance
• Generalized Dehn twists on surfaces and homology cylinders
• The handlebody group and the images of the second Johnson homomorphism
• Triviality of the $J_4$-equivalence among homology 3-spheres
• Universal Quadratic Forms and Untwisting Whitney Towers